We connect work done by Enochs, Rada and Hill in module approximation theory with work undertaken by several group theorists and algebraic topologists in the context of homotopical localization and cellularization of spaces. This allows one to consider envelopes and covers of arbitrary groups. We show some characterizing results for certain classes of groups, and present some open questions.
Cite this article
Sergio Estrada, José L. Rodríguez, Envelopes and covers for groups. Groups Geom. Dyn. 12 (2018), no. 1, pp. 107–120DOI 10.4171/GGD/440